Question: $\dfrac{d}{dx}(x^6+3x^4+7x^2)=$
Explanation: According to the sum rule, the derivative of $x^6+3x^4+7x^2$ is the sum of the derivatives of $x^6$, $3x^4$, and $7x^2$. The derivatives of these terms can be found using the power rule : $\dfrac{d}{dx}(x^n)=n\cdot x^{n-1}$ For example, this is the derivative of the first term: $\dfrac{d}{dx}(x^6)=6x^5$ Here is the complete differentiation process: $\begin{aligned} &\phantom{=}\dfrac{d}{dx}(x^6+3x^4+7x^2) \\\\ &=\dfrac{d}{dx}(x^6)+3\dfrac{d}{dx}(x^4)+7\dfrac{d}{dx}(x^2)&&\gray{\text{Basic differentiation rules}} \\\\ &=6x^5+3\cdot4x^3+7\cdot 2x&&\gray{\text{The power rule}} \\\\ &=6x^5+12x^3+14x \end{aligned}$ In conclusion, $\dfrac{d}{dx}(x^6+3x^4+7x^2)=6x^5+12x^3+14x$.